Abstract
The computation of quantum corrections to observables in quantum field theory requires making sense of expressions that are formally divergent. In this chapter we are going to show how this is done systematically. The renormalization program has nevertheless a much more profound meaning than just taming infinities.
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Notes
- 1.
The change from a quadratically to a logarithmically divergent integral is a consequence of the tensor structure (8.12) of the polarization tensor, and therefore a consequence of gauge invariance.
- 2.
This result has an interesting history. See, for example, [5].
- 3.
In a d-dimensional theory the canonical scaling dimensions of the fields coincide with its engineering dimension: \(\Delta={\frac{d-2}{2}}\) for bosonic fields and \(\Delta={\frac{d-1}{2}}\) for fermionic ones. For a Lagrangian with no dimensionful parameters classical scale invariance follows then from dimensional analysis.
- 4.
In the following we denote by \(\Lambda\) any regulator, not necessarily the momentum cutoff used in Sect. 8.1 By convention we consider that the removal of the regulator corresponds to the limit \(\Lambda\rightarrow\infty.\)
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Álvarez-Gaumé, L., Vázquez-Mozo, M.Á. (2012). Renormalization. In: An Invitation to Quantum Field Theory. Lecture Notes in Physics, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23728-7_8
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DOI: https://doi.org/10.1007/978-3-642-23728-7_8
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